Package 'mazeinda'

Associate pairwise vectors form one or two sets

Description

Given two matrices $m_1$ and $m_2$, computes all pairwise correlations of each vector in $m_1$ with each vector in $m_2$. Thanks to the package foreach, computation can be done in parallel using the desired number of cores.

Usage

associate(m1, m2, parallel = FALSE, n_cor = 1, estimator = "values", d1,
  d2, p11 = 0, p01 = 0, p10 = 0)

Arguments

m1, m2	matrices whose columns are to be correlated. If no estimation calculations are needed, default is NA.
parallel	should the computations for associating the matrices be done in parallel? Default is FALSE
n_cor	number of cores to be used if the computation is run in parallel. Default is 1
estimator	string indicating how the parameters $p_{11}$, $p_{01}$, $p_{10}$, $p_{00}$ are to be estimated. The default is 'values', which indicates that they are estimated based on the entries of x and y. If estimates=='mean', each $p_{ij}$ is estimated as the mean of all pairs of column vectors in $m_1$, and of $m_2$ if needed. If estimates=='own', the $p_{ij}$'s must be given as arguments.
d1, d2	sets of vectors used to estimate $p_{ij}$ parameters. If just one set is needed set $d_1$=$d_2$.
p11	probability that a bivariate observation is of the type (m,n), where m,n>0.
p01	probability that a bivariate observation is of the type (0,n), where n>0.
p10	probability that a bivariate observation is of the type (n,0), where n>0.

Details

To find pairwise monotonic associations of vectors within one set $m$, run associate($m$,$m$). Note that the values on the diagonal will not be necessarely 1 if the vectors contain 0's, as it can be seen by the formula $p_{11}^2 t_{11} + 2 * (p_{00} p_{11} - p_{01} p_{10})$

Value

matrix of correlation values.

Examples

v1=c(0,0,10,0,0,12,2,1,0,0,0,0,0,1)
v2=c(0,1,1,0,0,0,1,1,64,3,4,2,32,0)
associate(v1,v2)
m1=matrix(c(0,0,10,0,0,12,2,1,0,0,0,0,0,1,1,64,3,4,2,32,0,0,43,54,3,0,0,3,20,1),6)
associate(m1,m1)
m2=matrix(c(0,1,1,0,0,0,1,1,64,3,4,2,32,0,0,43,54,3,0,0,3,20,10,0,0,12,2,1,0,0),6)
associate(m1,m2)

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combine

Description

Designed to combine the matrix of correlation values with the matrix of p-values so that in the cases when the null hypothesis cannot be rejected with a level of confidence indicated by the significance, the correlation is set to zero. Thanks to the package foreach, computation can be done in parallel using the desired number of cores.

Usage

combine(m1, m2, sl = 0.05, parallel = FALSE, n_cor = 1,
  estimator = "values", d1, d2, p11 = 0, p01 = 0, p10 = 0)

Arguments

m1, m2	matrices whose columns are to be correlated. If no estimation calculations are needed, default is NA.
sl	level of significance for testing the null hypothesis. Default is 0.05.
parallel	should the computations for associating the matrices be done in parallel? Default is FALSE
n_cor	number of cores to be used if the computation is run in parallel. Default is 1
estimator	string indicating how the parameters $p_{11}$, $p_{01}$, $p_{10}$, $p_{00}$ are to be estimated. The default is 'values', which indicates that they are estimated based on the entries of x and y. If estimates=='mean', each $p_{ij}$ is estimated as the mean of all pairs of column vectors in $m_1$, and of $m_2$ if needed. If estimates=='own', the $p_{ij}$'s must be given as arguments.
d1, d2	sets of vectors used to estimate $p_{ij}$ parameters. If just one set is needed set $d_1$=$d_2$.
p11	probability that a bivariate observation is of the type (m,n), where m,n>0.
p01	probability that a bivariate observation is of the type (0,n), where n>0.
p10	probability that a bivariate observation is of the type (n,0), where n>0.

Details

To test pairwise monotonic associations of vectors within one set $m$, run combine($m$,$m$). Note that the values on the diagonal will not be necessarily significant if the vectors contain 0's, as it can be seen by the formula $p_{11}^2 t_{11} + 2 * (p_{00} p_{11} - p_{01} p_{10})$. The formula for the variance of the estimator proposed by Pimentel(2009) does not apply in case $p_{11}$, $p_{01}$,$p_{10}$, $p_{00}$ attain the values 0 or 1. In these cases the R function cor.test is used. Note that while independence implies that the estimator is 0, if the estimator is 0, it does not imply that the vectors are independent.

Value

matrix of combined association values and p-values.

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test_associations

Description

To test pairwise monotonic associations of vectors within one set $m$, run test_associations($m$,$m$). Note that the values on the diagonal will not be necessarily significant if the vectors contain 0's, as it can be seen by the formula $p_{11}^2 t_{11} + 2 * (p_{00} p_{11} - p_{01} p_{10})$. The formula for the variance of the estimator proposed by Pimentel(2009) does not apply in case $p_{11}$, $p_{00}$, $p_{01}$, $p_{10}$ attain the values 0 or 1. In these cases the R function cor.test is used. Note that while independence implies that the estimator is 0, the estimator being 0 does not imply that the vectors are independent.

Usage

test_associations(m1, m2, parallel = FALSE, n_cor = 1,
  estimator = "values", d1, d2, p11 = 0, p01 = 0, p10 = 0)

Arguments

m1, m2	matrices whose columns are used to estimate the $p_{ij}$ parameters. If no estimation calculations are needed, default is NA. Both are necessary if cross-correlating pairwise the vectors from two datasets.
parallel	should the computations for combiing the matrices be done in parallel? Default is FALSE.
n_cor	number of cores to be used if the computation is run in parallel. Default is 1.
estimator	string indicating how the parameters $p_{11}$, $p_{01}$, $p_{10}$, $p_{00}$ are to be estimated. The default is 'values', which indicates that they are estimated based on the entries of x and y. If estimates=='mean', each $p_{ij}$ is estimated as the mean of all pairs of column vectors in $m_1$, and of $m_2$ if needed. If estimates=='own', the $p_{ij}$'s must be given as arguments.
d1, d2	sets of vectors used to estimate $p_{ij}$ parameters. If just one set is needed set $d_1$=$d_2$.
p11	probability that a bivariate observation is of the type (m,n), where m,n>0
p01	probability that a bivariate observation is of the type (0,n), where n>0.
p10	probability that a bivariate observation is of the type (n,0), where n>0.

Details

Given two matrices $m_1$ and $m_2$, computes all pairwise correlations of each vector in $m_1$ with each vector in $m_2$. Thanks to the package foreach, computation can be done in parallel using the desired number of cores.

Value

matrix of p-values of association.

Examples

v1=c(0,0,10,0,0,12,2,1,0,0,0,0,0,1)
v2=c(0,1,1,0,0,0,1,1,64,3,4,2,32,0)
test_associations(v1,v2)
m1=matrix(c(0,0,10,0,0,12,2,1,0,0,0,0,0,1,1,64,3,4,2,32,0,0,43,54,3,0,0,3,20,1),6)
test_associations(m1,m1)
m2=matrix(c(0,1,1,0,0,0,1,1,64,3,4,2,32,0,0,43,54,3,0,0,3,20,10,0,0,12,2,1,0,0),6)
test_associations(m1,m2)
m3= matrix(abs(rnorm(36)),6)
m4= matrix(abs(rnorm(36)),6)
test_associations(m3,m4)

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